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og som Control paa det benyttede Kviksølvs Renbed dettes
Egenvægt ved ^ til 13.5963
samt Søvandets Yolumina ved forskjellige Temperaturer til
and, as a test of purity, the specific gravity of the
mercury at was found to be 13.5963, and
the volume of sea-water at different temperatures —
t° 0 8 13 ■7-5 2C
Vt af I i..000000 1.000308 1.000794 1.001654 1.003605 I.OO3227
Til Udjevning af den efter disse Observationer
optrukne Curve har jeg benyttet de mindste Kvadraters
Methode, iclet jeg har sat Ligningen for Søvandets Volum
ved t° under Formen
Vc = 1 + at + bt* + et3.
Betingelsesligningerne blive
a-\- 4 6 + 16 c — 0.000077 =0
a + 8 6 + 64 c — 0.00009925 = 0
«+13 6 -(- 169 c —0.00012723 =0
a + 17.56 + 306.25c — 0.000148857 = 0
a + 20 6 + 400 c — -0.00016135 = 0
hvoraf Systemerne
5a + 62.5 b -f- 955.25c — 0.000613687 = 0
62.5a + 955.25&+ 16132.37c — 0.008588 =0
955.25a-+ 16132.376 + 286702 c — 0.1392135 = 0
som ved Elimination giver
a = 0.0000527328
b-z 0.00000617375
c — — 0.000000037516
eller ved Afrunding
Vt—\+0.000052733*+0.0000061738^—0.00000003752^.
Efter denne Formel har jeg beregnet følgende Tabel,
hvori Søvandets Volum findes opført for hver hel Grad
ogsaa for Temperaturerne under 0°, uagtet Formelens
Gyldighed for dette Strøg ikke er støttet ved nogen
Observation.
t° o 4 8 13 17.5 20
Vt of I 1.000000 1.000308 1.000794 i.001654 1.002605 1.003227
For smoothing the curve laid down from these
observations, I adopted the method of the least squares, giving
the equation for the volume of the sea-water at t" the
form —
Vt = 1 + at + bt* + ct\
The conditional equations will be —
a + 4 &+ 16 c —0.000077 =0
a+ 8 6+ 64 c—0.00009925 =0
a + 13 b + 169 c — 0,00012723 = 0
a +-17.56 + 306.25c — 0.000148857 = 0
’a + 20 6 + 400 c — 0.00016135 = 0
from which are deduced —
5a + 62.5 6+ 955.25c — 0.000613687 = 0
62.5a + 955.256 + 16132.37c — 0.008588 -=0
955.25a + 16132.376 + 286702 c —0.1392135 =0
and these equations give by elimination —
a — 0.0000527328
b— 0.00000617375
c — — 0.000000037516
or, rounded off,
-7«=1 + 0.000052733^ + 0.0000061738£- — 0.00000003752^.
By means of this formula I determined the results
set forth in the following Table, which shows the volume
of sea-water, computed for every degree, including
temperatures below 0°, although the applicability of the formula
to the latter has not been ascertained from observation.
t° Vt t° Vt t° Vt
II I
—4 0.99989 5 i.00041 14 1.00185
—3 0.99990 6 1.00053 1.00205
— 2 0.99992 7 1.00066 16 1.00227
—i 0.99995 8 1.00080 17 1.00250
0 i.00000 9 1.00095 !7-5 1.00261
1 1.00006 10 1.00111 18 1.00273
2 i.00013 il 1.00128 19 1.00297
3 i.00021 12 1.00146 20 1.00322
4 1.00031 x3 1.00165
t’ V, t’ V, t" V,
—4 0.99989 5 i.00041 14 1.00185
—3 0.99990 6 1.00053 >5 1.00205
—2 0.99992 7 1.00066 16 1.00227
— i 0.99995 8 1.00080 17 1.00250
0 1.00000 9 1.00095 17-5 1.00261
i 1.00006 10 i.00111 18 1.00273
2 1.00013 11 1.00128 19 1.00297
3 1.00021 12 1.00146 20 1.00322
4 1.00031 13 1.00165
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